I know how to find the equation of the line tangent to a parabola through a certain point. But how do I find the equation of the parabola from the point and the tangent line? For example, how do I find the equation of the parabola that is tangent to the line $x+y-15=0$ at the point $(12,3)$?
2026-04-01 06:30:46.1775025046
Find the equation of parabola tangent to a line
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There are many parabolas with a given tangent line at a specific point on the line. For example, I’m sure you can find more than one parabola tangent to the line $y=0$ at the point $(0,0)$? The word “the” is tricky. It implicitly suggests there is only one such thing, but in this case, you can’t say “the” parabola, because there is more than one. A point and a slope determine a line, but a point and a slope do not determine a parabola.